"Based on the information available to us, we see no indications that Trump Tower was the subject of surveillance by any element of the United States government either before or after Election Day 2016," Republican Chairman Richard Burr and Senator Mark Warner, the committee's Democratic vice chairman, said in a statement.
The top Republican in Congress, House of Representatives Speaker Paul Ryan, on Thursday added his voice to those saying there was no sign of a wiretap.
But White House spokesman Sean Spicer forcefully defended Mr Trump's assertion during a briefing, citing media reports that have discussed intelligence collection on possible contacts between Trump associates and Russia in the campaign.
"There is no question that there were surveillance techniques used throughout this," Mr Spicer said.
When pressed for further evidence, Mr Spicer chastised the media for focussing so much attention on comments disparaging Mr Trump's claim about surveillance. He said reporters have not focussed enough on comments from officials denying evidence of any collusion between Russia and the Trump campaign.
The Russian government has rejected an accusation by US intelligence agencies that it worked to influence the election in Mr Trump's favour by hacking computer systems, among other methods.
House Speaker Ryan told reporters: "The point is, the intelligence committees in their continuing, widening, ongoing investigation of all things Russia, got to the bottom - at least so far - with respect to our intelligence community that - that no such wiretap existed."
An official familiar with the investigations by Congress and intelligence and law enforcement agencies said investigators have looked as aggressively and thoroughly as they can for evidence of any spying on Mr Trump or his associates but have found none.
Mr Trump, a Republican, made the accusation six weeks after he took over the presidency from Democrat Barack Obama.
Mr Trump accused Mr Obama of wiretapping him during the late stages of the campaign, but provided no evidence. Mr Obama said through a spokesman that it was "simply false."
"How low has President Obama gone to tap my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!," Mr Trump wrote.
At least four congressional committees added the startling accusation in their investigations of possible Russian meddling in the election campaign and Russian ties to Mr Trump and his associates.
On Wednesday, House of Representatives Intelligence Committee Chairman Devin Nunes, a Republican, and top Democrat Adam Schiff told reporters they had seen no evidence that Trump Tower was tapped and said they would ask Federal Bureau of Investigation Director James Comey about the issue during a public hearing on Monday.
Mr Ryan told reporters he received the same intelligence briefing as Mr Nunes and Mr Schiff.
Mr Trump appeared to back away from his accusation of wiretapping in a Fox News interview on Wednesday night.
"But wiretap covers a lot of different things. I think you're going to find some very interesting items coming to the forefront over the next two weeks," Mr Trump said.